A set of agents (human or computer process) are supposed to decide on an action given a finite set of possible strategies when the background information is vague or numerically imprecise. The agents evaluate the strategies and communicate their opinions about their utilities, their opinions about the credibilities of the reports of the other agents, as well as their opinions of the reliabilities of the other agents. A significant property of the theory is that it admits the representation of imprecise information at all stages. The strategies are evaluated relative to generalisations of the principle of maximising the expected utility. It is also demonstrated how decision trees can be integrated into the framework and suggest an evaluation rule taking into account all strategies, credibilities, reliabilities, probabilities and utilities involved in the framework. This is done without presupposing the existence of a central co-ordinating agent that evaluates the different reports of the agents. In a distributed context there are no a priori reasons for such an agent and we show how it can be eliminated in our framework.